A094567 Associated with alternating row sums of array in A094566.

1, 4, 30, 203, 1394, 9552, 65473, 448756, 3075822, 21081995, 144498146, 990405024, 6788337025, 46527954148, 318907342014, 2185823439947, 14981856737618, 102687173723376, 703828359326017, 4824111341558740, 33064951031585166, 226630545879537419

Offset

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (6,6,-1).

Formula

a(n) = F(4n+1) - a(n-1) for n >= 1, with a(0) = 1.

a(n) = (Fib(4n+3) + (-1)^n)/3. - Ralf Stephan, Dec 04 2004

a(n) = 6*a(n-1)+6*a(n-2)-a(n-3), with a(0)=1, a(1)=4, a(2)=30. - Harvey P. Dale, Jul 13 2011

G.f.: (1-2*x)/(1-6*x-6*x^2+x^3). - Harvey P. Dale, Jul 13 2011

a(n) = (-1)^n*sum((-1)^k*Fibonacci(4*k+1), k=0..n). - Gary Detlefs, Jan 22 2013

a(n) = (2^(-n)*(5*(-2)^n+(7-3*sqrt(5))^n*(5-2*sqrt(5))+(5+2*sqrt(5))*(7+3*sqrt(5))^n))/15. - Colin Barker, Mar 05 2016

Example

Obtain 4,30,203 from a(0)=1 and Fibonacci numbers 1,5,34,233: 4=5-1, 30=34-4, 203=233-30.

Mathematica

RecurrenceTable[{a[0]==1, a[n]==Fibonacci[4n+1]-a[n-1]}, a[n], {n, 30}] (* or *) LinearRecurrence[{6, 6, -1}, {1, 4, 30}, 31] (* Harvey P. Dale, Jul 13 2011 *)

Prog

(PARI) Vec(-(2*x-1)/((x+1)*(x^2-7*x+1)) + O(x^100)) \\ Colin Barker, Nov 19 2014
(PARI) vector(30, n, n--; (fibonacci(4*n+3) + (-1)^n)/3) \\ Michel Marcus, Nov 19 2014

Crossrefs

Cf. A000045, A094566.

Sequence in context: A268218 A272493 A246151 * A134093 A007905 A084976

Adjacent sequences: A094564 A094565 A094566 * A094568 A094569 A094570

Keyword

nonn,easy

Author

Clark Kimberling, May 12 2004

Extensions

More terms from Harvey P. Dale, Jul 13 2011

Status

approved